2,517 research outputs found
Billiards with polynomial mixing rates
While many dynamical systems of mechanical origin, in particular billiards,
are strongly chaotic -- enjoy exponential mixing, the rates of mixing in many
other models are slow (algebraic, or polynomial). The dynamics in the latter
are intermittent between regular and chaotic, which makes them particularly
interesting in physical studies. However, mathematical methods for the analysis
of systems with slow mixing rates were developed just recently and are still
difficult to apply to realistic models. Here we reduce those methods to a
practical scheme that allows us to obtain a nearly optimal bound on mixing
rates. We demonstrate how the method works by applying it to several classes of
chaotic billiards with slow mixing as well as discuss a few examples where the
method, in its present form, fails.Comment: 39pages, 11 figue
The nature of compensatory and restorative processes in the livers of animals irradiated during hypokinesia
The nature of postirradiation repair in the livers of rats irradiated during hypokinesia is investigated. Hepatocyte population counts, mitotic activity, binuclear cell content, and karyometric studies were done to ascertain the effects of combined hypokinesia and radiation. Hypokinesia is shown to change the nature and rate of post-irradiation changes in the liver, the effect varying with the timing of irradiation relative to the length of hypokinesia. It is concluded that the changes in the compensatory and restorative processes are caused by stress developed in response to isolation and restricted mobility. By changing neuroendocrine system activity, the stress stimulates cell and tissue repair mechanisms at a certain stage essential to the body's reaction of subsequent irradiation
Basic principles of hp Virtual Elements on quasiuniform meshes
In the present paper we initiate the study of Virtual Elements. We focus
on the case with uniform polynomial degree across the mesh and derive
theoretical convergence estimates that are explicit both in the mesh size
and in the polynomial degree in the case of finite Sobolev regularity.
Exponential convergence is proved in the case of analytic solutions. The
theoretical convergence results are validated in numerical experiments.
Finally, an initial study on the possible choice of local basis functions is
included
Exponential speed of mixing for skew-products with singularities
Let be the
endomorphism given by where is a positive real number. We prove that is
topologically mixing and if then is mixing with respect to Lebesgue
measure. Furthermore we prove that the speed of mixing is exponential.Comment: 23 pages, 3 figure
Spatial Structure of Stationary Nonequilibrium States in the Thermostatted Periodic Lorentz Gas
We investigate analytically and numerically the spatial structure of the
non-equilibrium stationary states (NESS) of a point particle moving in a two
dimensional periodic Lorentz gas (Sinai Billiard). The particle is subject to a
constant external electric field E as well as a Gaussian thermostat which keeps
the speed |v| constant. We show that despite the singular nature of the SRB
measure its projections on the space coordinates are absolutely continuous. We
further show that these projections satisfy linear response laws for small E.
Some of them are computed numerically. We compare these results with those
obtained from simple models in which the collisions with the obstacles are
replaced by random collisions.Similarities and differences are noted.Comment: 24 pages with 9 figure
- …